Regularization of the Solution of the Cauchy Problem for a Linear Stationary System of Navier-Stokes Equations in an Unbounded Domain

E. Y. Jabborov

E. Y. Jabborov Samarkand State University named after Sharof Rashidov, University Boulevard, 15, Samarkand, 140104,Uzbekistan,

Keywords: Cauchy problem, Navier--Stokes system of equations, Laplace equations, Carleman function, fundamental solutions, Green formula, regularization

Abstract

This paper is devoted to the study of the continuation of the solution of the Cauchy problem for a linear stationary system of Navier-Stokes equations in the domain $D$ according to its known values on the smooth part of the boundary . It is required to determine a solution in the domain based on the Cauchy data on a part of the boundary of the domain, i.e. solve the problem of analytical continuation of the solution of a linear stationary system of Navier-Stokes equations in an unbounded spatial domain. Using the Carleman function method, we construct an approximate solution of the Cauchy problem for a linear stationary system of Navier--Stokes equations, according to the Cauchy data on a part of the domain boundary. If the Carleman function is constructed, then using Green formula, one can find a regularized solution in an explicit form.

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